This thesis describes the first successful growth of boron δ layers using silicon MBE. SIMS has been used to demonstrate that the layer widths are ∽2nm as has been confirmed by TEM. This is probably an overestimate, an average value of (0.3+-0.5)nm being obtained from XRD, suggesting that these are the thinnest 6 layers produced to date. Hall and XRD measurements indicate that the boron dopant is fully activated up to sheet coverages of 1/2 monolayer, i. e. ∽3.5x10^14cm-2. The CV profile obtained for a B δ layer of sheet density 2.5x10^12cm-2 has FWHM ∽3nm, a result which is shown to be consisitent with δ doping in the light of recent theoretical work. Resistivity, magnetoresistance and the Hall effect have been measured at temperatures down to 0.3K using magnetic fields of up to 12T on samples of sheet density in the range 4x10^12cm-2 to 8x10^13cm-2. 2D weak localisation and associated electron-electron interaction effects have been observed in samples of sheet density above 1.8x10^13cm-2 with evidence of spin-orbit scattering. These samples are shown to undergo a "metal-insulator" transition in high magnetic fields with variable range hopping at 12T. Samples of sheet density ≤ 1x10^13cm-2, show activated transport from which it is concluded that the critical acceptor separation for the metal-insulator transition in this system is significantly less than the value found in bulk, uniformly doped, Si:B. It is suggested that this may be due to the splitting of the valence band degeneracy due to quantum confinement.